Does bootstrapping the remainder component of seasonal time series improve forecasting using SARIMA model? An application to rainfall data

Many time series exhibit both trends and seasonal patterns. Accounting accurately for such seasonal patterns in time series goes a long way to improve forecasting accuracy of seasonal time series models such as seasonal autoregressive integrated moving average (SARIMA) model. Even though SARIMA model has frequently been used to forecast seasonal time series, it does not provide accurate forecast when the time series data is sparse. To address data sparsity in seasonal time series before modelling and forecasting using SARIMA, the remainder component of the time series is extracted, bootstrapped and added back to the trend and seasonal components. This proposed procedure is described in this study as moving block bootstrapping-based SARIMA (MBB-SARIMA) model. The MBB-SARIMA is fitted to synthetic monthly and quarterly seasonal time series data of sample sizes 50, 100 and 300, alongside DS-SARIMA (modelling components of decomposed time series and adding back the fitted components without bootstrapping the remainder components) and OS-SARIMA (modelling the original time series without decomposing the time series into components) models. The forecasting accuracy of these models are compared through Monte Carlo simulation at 1000 repetitions. The results from the Monte Carlo simulation reveal that the proposed MBB-SARIMA model performs better than the DS-SARIMA and OS-SARIMA models at all the sample sizes in terms of forecasting and has low forecasting uncertainty. The results further show that each model improves its forecasting performance when the sample size increases from 50 to 100 and from 100 to 300. The proposed MBB-SARIMA model is applied to real average monthly rainfall data of Ghana in West African which spans from January 1984 to December 2020. The results show that MBB-SARIMA (1,1,1)(1,1,1)12 is the best candidate model to predict rainfall pattern in Ghana with minimum AIC value of − 162.07. The MBB-SARIMA, compared with the DS-SARIMA and OS-SARIMA models, performs better in terms of forecasting with low forecast uncertainty, having minimum values of root mean square error (RMSE) and mean absolute percentage error (MAPE), respectively, as 0.1945 and 3.6022.